I don't think any mentioned that these chicks had Coccidiosis? Coccidia are protozoa.
What was discussed in this thread was Omphalitis/Mushy chick disease or similar which is a bacterial infection in the yolk sac.
As for the photo -
I re-posted that asking for clarification of what we were seeing. The vent
is at the base of the tail in her photo. OP did confirm that fecal matter was coming from the Navel and has explained the 2X. Poop would naturally run down because of gravity.

And yes, a chick can live that long with fecal matter coming out of the navel, sadly, I have seen some people keep chicks alive for a week with an unabsorbed egg yolk or even intestines hanging out, the possibility is real.
Take a look at this photo, the yolk sac is not completely absorbed, but fecal matter is not coming out of it. Note the
Vent is at the base of the tail
View attachment 1507581
Photo reference
https://the-chicken-chick.com/pasty-butt-in-chicks-causestreatmen/